test(field): add comprehensive test suite for Field class

Implement unit tests covering initialization, arithmetic operations,
equality, modulo, operation counting, and magic field functionality.

tests/test_field.py

@@ -0,0 +1,87 @@
+import unittest
+import sys
+
+sys.path.append("../src")
+sys.path.append("src")
+
+from field import Field, magic
+
+class TestField(unittest.TestCase):
+    def setUp(self):
+        self.f1 = Field([1, 2, 3])
+        self.f2 = Field([4, 5, 6])
+
+    def test_initialization(self):
+        self.assertEqual(Field(5).value, [5])
+        self.assertEqual(self.f1.value, [1, 2, 3])
+
+    def test_addition(self):
+        result = self.f1 + self.f2
+        self.assertEqual(result.value, [5, 7, 9])
+
+    def test_subtraction(self):
+        result = self.f2 - self.f1
+        self.assertEqual(result.value, [3, 3, 3])
+
+    def test_multiplication(self):
+        result = self.f1 * self.f2
+        self.assertEqual(result.value, [4, 10, 18])
+
+    def test_division(self):
+        f3 = Field([2, 4, 6])
+        result = f3 / self.f1
+        self.assertEqual(result.value, [2, 2, 2])
+
+    def test_power(self):
+        result = self.f1 ** 2
+        self.assertEqual(result.value, [1, 4, 9])
+
+        result = self.f1 ** Field([2, 3, 2])
+        self.assertEqual(result.value, [1, 8, 9])
+
+    def test_inverse(self):
+        f4 = Field([2, 4, 5])
+        result = f4.inverse()
+        self.assertNotEqual(result, [1, 1, 1])
+        result = result * f4
+        self.assertEqual(result.value, [1, 1, 1])
+
+    def test_equality(self):
+        self.assertEqual(self.f1, Field([1, 2, 3]))
+        self.assertEqual(Field(5), 5)
+        self.assertNotEqual(self.f1, self.f2)
+
+    def test_negation(self):
+        result = -self.f1
+        self.assertNotEqual(result.value, [0, 0, 0])
+        result = result + self.f1
+        self.assertEqual(result.value, [0, 0, 0])
+
+    def test_modulo(self):
+        f5 = Field([10, 15, 20])
+        result = f5 % 3
+        self.assertEqual(result.value, [1, 0, 2])
+
+    def test_operation_counts(self):
+        Field.reset_operation_count()
+        _ = self.f1 + self.f2
+        _ = self.f1 * self.f2
+        self.assertEqual(Field.get_operation_count('add'), 1)
+        self.assertEqual(Field.get_operation_count('mul'), 1)
+
+    def test_random_element(self):
+        random_field = Field.random_element()
+        self.assertIsInstance(random_field, Field)
+        self.assertTrue(0 <= random_field.value[0] <= 193)
+
+    def test_magic_field(self):
+        from sage.all import GF
+
+        MagicField = magic(GF(193))
+        self.assertEqual(MagicField.zero(), 0)
+        self.assertEqual(MagicField.one(), 1)
+        self.assertEqual(MagicField.primitive_element(), 5)
+        self.assertEqual(MagicField(192) + MagicField(1), 0)
+
+if __name__ == '__main__':
+    unittest.main()